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Polytypic Values Possess Polykinded Types
, 2000
"... A polytypic value is one that is defined by induction on the structure of types. In Haskell the type structure is described by the socalled kind system, which distinguishes between manifest types like the type of integers and functions on types like the list type constructor. Previous approaches to ..."
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Cited by 107 (20 self)
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A polytypic value is one that is defined by induction on the structure of types. In Haskell the type structure is described by the socalled kind system, which distinguishes between manifest types like the type of integers and functions on types like the list type constructor. Previous approaches to polytypic programming were restricted in that they only allowed to parameterize values by types of one fixed kind. In this paper we show how to define values that are indexed by types of arbitrary kinds. It appears that these polytypic values possess types that are indexed by kinds. We present several examples that demonstrate that the additional exibility is useful in practice. One paradigmatic example is the mapping function, which describes the functorial action on arrows. A single polytypic definition yields mapping functions for datatypes of arbitrary kinds including first and higherorder functors. Polytypic values enjoy polytypic properties. Using kindindexed logical relations we prove...
Generic Haskell: practice and theory
 In Generic Programming, Advanced Lectures, volume 2793 of LNCS
, 2003
"... Abstract. Generic Haskell is an extension of Haskell that supports the construction of generic programs. These lecture notes describe the basic constructs of Generic Haskell and highlight the underlying theory. Generic programming aims at making programming more effective by making it more general. ..."
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Cited by 65 (23 self)
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Abstract. Generic Haskell is an extension of Haskell that supports the construction of generic programs. These lecture notes describe the basic constructs of Generic Haskell and highlight the underlying theory. Generic programming aims at making programming more effective by making it more general. Generic programs often embody nontraditional kinds of polymorphism. Generic Haskell is an extension of Haskell [38] that supports the construction of generic programs. Generic Haskell adds to Haskell the notion of structural polymorphism, the ability to define a function (or a type) by induction on the structure of types. Such a function is generic in the sense that it works not only for a specific type but for a whole class of types. Typical examples include equality, parsing and pretty printing, serialising, ordering, hashing, and so on. The lecture notes on Generic Haskell are organized into two parts. This first part motivates the need for genericity, describes the basic constructs of Generic Haskell, puts Generic Haskell into perspective, and highlights the underlying theory. The second part entitled “Generic Haskell: applications ” delves deeper into the language discussing three nontrivial applications of Generic Haskell: generic dictionaries, compressing XML documents, and a generic version of the zipper data type. The first part is organized as follows. Section 1 provides some background discussing type systems in general and the type system of Haskell in particular. Furthermore, it motivates the basic constructs of Generic Haskell. Section 2 takes a closer look at generic definitions and shows how to define some popular generic functions. Section 3 highlights the theory underlying Generic Haskell and discusses its implementation. Section 4 concludes. 1
Typing Haskell in Haskell
 Haskell Workshop
, 1999
"... Haskell benefits from a sophisticated type system, but implementors, programmers, and researchers suffer because it has no formal description. To remedy this shortcoming, we present a Haskell program that implements a Haskell typechecker, thus providing a mathematically rigorous specification in a n ..."
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Cited by 51 (2 self)
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Haskell benefits from a sophisticated type system, but implementors, programmers, and researchers suffer because it has no formal description. To remedy this shortcoming, we present a Haskell program that implements a Haskell typechecker, thus providing a mathematically rigorous specification in a notation that is familiar to Haskell users. We expect this program to fill a serious gap in current descriptions of Haskell, both as a starting point for discussions about existing features of the type system, and as a platform from which to explore new proposals.
Memo Functions, Polytypically!
 Proceedings of the 2nd Workshop on Generic Programming, Ponte de
, 2000
"... . This paper presents a polytypic implementation of memo functions that are based on digital search trees. A memo function can be seen as the composition of a tabulation function that creates a memo table and a lookup function that queries the table. We show that tabulation can be derived from ..."
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Cited by 13 (5 self)
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. This paper presents a polytypic implementation of memo functions that are based on digital search trees. A memo function can be seen as the composition of a tabulation function that creates a memo table and a lookup function that queries the table. We show that tabulation can be derived from lookup by inverse function construction. The type of memo tables is dened by induction on the structure of argument types and is parametric with respect to the result type of memo functions. A memo table for a xed argument type is then a functor and lookup and tabulation are natural isomorphisms. We provide simple polytypic proofs of these properties. 1 Introduction A memo function [11] is like an ordinary function except that it caches previously computed values. If it is applied a second time to a particular argument, it immediately returns the cached result, rather than recomputing it. For storing arguments and results a memo function internally employs an index structure, the ...